Multispecies Weighted Hurwitz Numbers

The construction of hypergeometric $2D$ Toda $\tau$-functions as generating functions for weighted Hurwitz numbers is extended to multispecies families. Both the enumerative geometrical significance of multispecies weighted Hurwitz numbers, as weighted enumerations of branched coverings of the Riemann sphere, and their combinatorial significance in terms of weighted paths in the Cayley graph of $S_n$ are derived. The particular case of multispecies quantum weighted Hurwitz numbers is studied in detail.Comment: this is substantially enhanced version of arXiv:1410.881

Multispecies quantum Hurwitz numbers

The construction of hypergeometric 2D Toda $\tau$-functions as generating functions for quantum Hurwitz numbers is extended here to multispecies families. Both the enumerative geometrical significance of these multispecies quantum Hurwitz numbers as weighted enumerations of branched coverings of the Riemann sphere and their combinatorial significance in terms of weighted paths in the Cayley graph of $S_n$ are derived.Comment: 11 pages.This is the revised version posted March 30, 201

Multispecies virial expansions

We study the virial expansion of mixtures of countably many different types of particles. The main tool is the Lagrange–Good inversion formula, which has other applications such as counting coloured trees or studying probability generating functions in multi-type branching processes. We prove that the virial expansion converges absolutely in a domain of small densities. In addition, we establish that the virial coefficients can be expressed in terms of two-connected graphs

ON THERMODYNAMICS OF MULTISPECIES ANYONS

We address the problem of multispecies anyons, i.e. particles of different species whose wave function is subject to anyonlike conditions. The cluster and virial coefficients are considered. Special attention is paid to the case of anyons in the lowest Landau level of a strong magnetic field, when it is possible (i) to prove microscopically the equation of state, in particular in terms of Aharonov-Bohm charge-flux composite systems, and (ii) to formulate the problem in terms of single-state statistical distributions.Comment: Latex, 19 page

Managing Ambiguous Amphibians: Feral Cows, People, and Place in Ukraine’s Danube Delta

This paper analyzes how a herd of feral cattle emerged in the core zone of Ukraine’s Danube Biosphere Reserve and why it still exists despite numerous challenges to the legality of its presence there. Answering these questions requires an analytical approach that begins from the premise that animals, plants, substances, documents, and technologies are active participants in making social and political worlds rather than passive objects of human intervention and manipulation. Drawing together insights from multispecies ethnography, animal geography, amphibious anthropology, and studies of nature protection in former Soviet republics, the author argues that the feral cattle exist because they are part of an amphibious multispecies assemblage in which relations among cattle, elements of the delta’s wetland ecologies, legal norms, and the Reserve managers’ documentation practices have aligned to create an autonomous space for cattle to dwell with minimal human intervention

Interacting families of Calogero-type particles and SU(1,1) algebra

We study a one-dimensional model with F interacting families of Calogero-type particles. The model includes harmonic, two-body and three-body interactions. We emphasize the universal SU(1,1) structure of the model. We show how SU(1,1) generators for the whole system are composed of SU(1,1) generators of arbitrary subsystems. We find the exact eigenenergies corresponding to a class of the exact eigenstates of the F-family model. By imposing the conditions for the absence of the three-body interaction, we find certain relations between the coupling constants. Finally, we establish some relations of equivalence between two systems containing F families of Calogero-type particles.Comment: 16 pages, no figures, to be published in Mod.Phys.Lett.

Calogero Model(s) and Deformed Oscillators

We briefly review some recent results concerning algebraical (oscillator) aspects of the $N$-body single-species and multispecies Calogero models in one dimension. We show how these models emerge from the matrix generalization of the harmonic oscillator Hamiltonian. We make some comments on the solvability of these models.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA